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- W1635007975 abstract "We list the subgroups of the basis set of Cl3,0 and classify them according to three criteria for construc- tion of universal Clifford algebras: (1) each generator squares to ±1, (2) the generators within the group anti- commute, and (3) the order of the resulting group is 2 n+1 , where n is the number of nontrivial generators. Obedi- ent groups we call choirs; disobedient groups, bands. We classify choirs by modes and bands by rhythms, based on canonical equality. Each band generator has a trans- position (number of other generators it commutes with). The band's transposition signature is the band's chord. The sum of transpositions divided by twice the number of generator pair combinations is the band's beat. The band's order deviation is the band's disorder. For n ≤ 3, we show that the Cl3,0 basis set has 21 non-isomorphic subgroups consisting of 9 choirs and 12 bands." @default.
- W1635007975 created "2016-06-24" @default.
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- W1635007975 date "2008-09-02" @default.
- W1635007975 modified "2023-09-27" @default.
- W1635007975 title "Taxonomy of Clifford Cl_{3,0} subgroups: Choir and band groups" @default.
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